Fertilizers supply nutrients to the soil needed to produce various crops. The most common nutrients in soil are nitrogen, phosphorous and potassium. In addition, some crops require micronutrients, such as zinc (Zn) and iron (Fe), depending on soils. Fertilizer of course costs money, but the risk of lower yields resulting from under-fertilizing has in the past generally outweighed the monetary cost of over-fertilizing. Because the production of nitrogen supplying fertilizers typically requires natural gas, the volatility in natural gas pricing can cause nitrogen fertilizer prices to escalate unpredictably. In addition, the overuse of fertilizer creates the potential for negative environmental consequences, and so from an environmental perspective too it is desirable to minimize the application of fertilizers. Some governments in fact, in Europe for the most part, closely regulate the amount of fertilizers that farmers apply.
A conventional method for calculating nitrogen needs for a field involves the following equation:NFERT=NCROP−NRES.SOIL−(NOM+NPREV.CROP+NMANURE)−NIRR
where: NFERT=fertilizer N recommendation                NCROP=yield goal×N yield factor        NRES.SOIL=preplant soil profile NO3−content (or residual soil)        NOM=organic N mineralization        NPREV.CROP=legume N availability        NMANURE=manure N availability        NIRR=irrigation water N availabilityHavlin et al., Soil Fertility and Fertilizers, 1999, Prentice Hall, New Jersey, at pages 350–51. The equation above differs from that provided in Havlin et al., in that the equation above factors in the availability of N from irrigation water (NIRR). As discussed by Havlin et al. on page 351, NCROP represents the nitrogen required by the crop and involves predicting the crop yield and the nitrogen needed to produce that yield. A measure of “biomass,” which is basically the density or amount of plant-life, is known to be directly related to crop yield. One measure of biomass for crops such as corn and soybeans is known as “leaf area index” (LAI), which can be measured in at least two ways. First, LAI can be measured directly by taking all the crop leaves from a unit field area and measuring in a laboratory the total area of one side of the leaves using an area meter. Another way by which LAI can be derived is from remotely sensed data using a canopy reflectance model. See Kuusk, “A Fast, Invertible Canopy Reflectance Model,” in Remote Sensing of Environment, 51:342–50 (1995); Verhoef, “Light Scattering by Leaf Layers with Application to Canopy Reflectance Modeling: The SAIL Model,” in Remote Sensing of Environment, 16:125–41 (1984). The later method is non-destructive to the crops and suitable for agricultural field management.        
Precision farming techniques utilizing, for example, Global Positioning System (GPS) technology has found many uses, one being the application of fertilizers in agricultural fields, as is described, for example, in U.S. Pat. No. 5,220,876 to Monson et al. The '876 Patent describes a variable-rate fertilizer application system. The system has a digital map characterizing the field's soil types. The system also has other maps that characterize the desired level of various fertilizer types to be applied upon the field. The patent states that the levels of fertilizer can be determined from predefined characteristics, such as existing fertilizer levels, field topography or drainage studies. A processor calculates and controls the dispensing of the various fertilizers based on both the soil map and the fertilizer map. A position locator on the vehicle dispensing the fertilizers provides the necessary location information to apply the prescribed amount of fertilizer in the correct location. Related U.S. Pat. No. 5,355,815 to Monson describes a closed-loop fertilizer application system, which also varies the application rate, but which does not require maps of current fertilizer levels. The system is said to be able to determine a chemical prescription in real-time for a soil scene, depending on the existing soil fertilizer content ascertained by a real-time soil analyzer. The system then dispenses fertilizer in response to the prescription.
Another variable-rate fertilizer application system is described in U.S. Pat. No. 4,630,773 to Ortlip. The '773 Patent describes a system that applies fertilizer according to the specific needs of each individual soil type of soil comprising a field. The patent also describes the assembly of a digital soil map for a field to be fertilized. An aerial infrared photograph of the field is taken. The patent states that the different shades in the photograph correspond to different moisture contents of the soil types. The photograph is digitized into an array of pixels. Each pixel is assigned a digital value based on the shading in the photograph, such that the value is representative of the soil type the pixel represents. The application of fertilizer is varied according to the digital soil map.
The maximum possible crop yield—that is, “yield goal,” which factors into the calculation of NCROP in the equation above—that a particular location in a field is able to attain may vary from location to location. For example, there may be a patch of gravel in a field, and no matter how much nitrogen-based fertilizer is added to that location, the yield in that location will not increase. The gravel may cause only weeds to grow at that location, or may hinder the growth of any vegetation. Gravel may be on the surface, or may be at a shallow level below the surface. The gravel may not be detectable from a soil image. Other factors that may vary the yield at a particular location in a field, but which also may not be detectable from a soil image, are the soil's fertility and its pH content. Despite this potential variation in yield throughout a single field, the prior art variable-rate fertilizer application systems of which the present inventors are aware all employ a single yield goal measure for a field.